Improving the efficiency of using multivalued logic tools: application of algebraic rings

Area of Science:

• Information Technology
• Abstract Algebra
• Multivalued Logic Systems

Background:

• Modern information technologies require efficient integration of abstract algebra methods.
• Existing methods for multivalued logics often lack a direct algebraic connection, limiting efficiency.
• Previous work established algebraic expressions in Galois fields for prime-valued logic variables and an algebraic δ-function for powers of primes.

Purpose of the Study:

• To establish an explicit connection between algebraic operations and operations in multivalued logics.
• To extend the applicability of the algebraic δ-function to multivalued logic variables where the number of values is p-1 (p being a prime number).
• To demonstrate the reduction of logical operations to algebraic expressions using the defined algebraic δ-function.

Main Methods:

• Development of an algebraic δ-function applicable to multivalued logic variables with p-1 values.
• Demonstration of reducing logical operations to algebraic expressions.
• Experimental validation using electronic circuits to prove the approach's adequacy.

Main Results:

• Successfully defined an algebraic δ-function for multivalued logic variables taking p-1 values.
• Showcased the function's ability to translate logical operations into algebraic expressions.
• Presented constructive examples and experimental results confirming the approach's effectiveness.

Conclusions:

• The proposed algebraic δ-function effectively bridges abstract algebra and multivalued logic operations for p-1 valued systems.
• This approach enhances the efficiency of using abstract algebra in information technologies.
• The findings are supported by constructive examples and experimental validation.